input-output

In this brief, the extraction of frequency responses of a magnetic levitated open-loop unstable plant operating in a closed-loop, employing the Empirical Transfer Function Estimate (ETFE) approach is presented. Frequency responses of the closed-loop transfer function, loop-gain, and the plant are obtained by injection of an eigenfrequency-rich excitation signal. Consequently, measuring the levitated beam’s displacement between a pair of electromagnets. The mathematical model derived via the first principle is compared with the estimated frequency response. The experimentally obtained open-loop gain, capturing important unmodelled system dynamics, will be utilized for robust control design via loop-shaping. Thus, the proposed approach is amenable to robust control design without relying on complex control algorithms.